
2
∂∨TM⊇ ??⊆R∪ !⇔⊇??R ?
∀ ?I R ♣R∪∧TM ∨I ?
≡∨TMⓒ∧ ? ∈?∪ ⓒ∧ ∨?⇔?
⊂ TM ?G I∪? #∃∪ ∪⇒∨? ⇔? ∝?? ⓒ
∂∨TM⊇ ??⊆R∪
%⇔⊇??R ?
∂∨TM⊇ ??⊆R∪
!⇔⊇??R ?
∂ &∀∋′&∂&∋( (
..........................2
∂ & &?(
.......................................3
∀ ?I R
♣R∪∧TM ∨I ?
↓R∧∪∈?
⊂R
∧TM
∧??R↓R∪∨∪⇔∧ ∨∪TM
∧TM
⇔ ⇔∧ ⊂?∧TM
.............................4
↓R∧∪∈?
⊂R
∧TM
∧??R↓R∪∨∪⇔∧ ∨∪TM
∧TM
⇔ ⇔∧ ⊂?∧TM
.......................................5
∂
ⓒ?
↓∨?⇔∪⊂TM#TM∪R ∧R
∧TM
∈TM ⊂#
∀#∪?TMI
∃∨⇒#TM
♣R∪∧TM ∨I ?
........7
⊂#??∨ ⊂?∧∪∈?
↓?∨?∈∧?∨∪⇔∧∪∈?
.........................................................)2
≡∨TMⓒ∧ ?
∈?∪
ⓒ∧ ∨?⇔?
≡∨TMⓒ∧ ?
∈?∪
⇔ ⓒ∧ ∨?⇔?
∧TM
∈?∪⊂?∧∪⇔∧∪∈TM
⊂?↓?ⓒ ⊂?∧TM ..........)6
∧?ⓒ
∧TM
∈?∪⊂?∧∪⇔∧∪∈⇒
⊂?↓?ⓒ?⊂?
Rⓒ
#∨⇒∈R∪∧?∪
ⓒ?
↓∨?⇔∪⊂TM#TM∪??R
I∪?
#TM?
∈?∪∨⇒......................................)8
⊂ TM ?G
I∪?
∧?
?R∪∧TM ∨I ?
.........................................................)8
⊂ TM ?G
I∪?
#∃∪ ∪⇒∨? ⇔?
∝?? ⓒ
∂∨∪ⓒ
?∧ ⇔R∧R
⇔G∨ ∪
................)9
°∪?
ⓒ?
?#TM⊇R ↓?R
TM
∧∨? ⊂?∧∪⇔⊂⇒
∧TM
↓∨ ⇔∧?
∈?∪
??? ⓒ
?∧⇒⊂ ⓒ
#∨G#R∪
ⓒ?
∧?∨TM ⓒ∧?∪
TM∪
R⊆
TM ?I R .
(
???TM
?R∪∧TM ∨I ?
?⇒I
?IⓒTM∪?
?⊂G?R∪?
⊂#TM∨R
ⓒ?
#∨TM∈??G⇔R∪
∧∨? ⊂?∧∪⇔⊂⇒
?⊂∪?.
(
⇔TM ?∨⇒∧?∧?
∈?∧?∧?⇔⇔R∧?∪
⇔R
∈?∧?ITM∨ R
⇔ ⊂⊇ ⓒ?
⊂R
∧∪
R⊆
Rⓒ R ⊆R∪ .
∃TM
⇔ ⊂ TM?TM
R ↓ⓒR∪
∧TM
Rⓒ R↓⇒⊂RⓒTM
??ⓒ?∧TM
⇔TM ?∨TM
∧∨? ⊂?∧∪⇔⊂TM .
∃TM
⇔ ⊂ TM?TM
R ↓ⓒR∪
∧TM
Rⓒ R↓⇒⊂RⓒTM
⊂⇒ⓒTM
?∪∈
?⊂∪? .
∝? R∧R
∈?ⓒTMⓒ∪∈?
∧TM
⊇∪
⇔∧?ⓒ
%∨ ?.
♠?
? R∧R
⇔R
?R∪∧TM ∨I ?
TM ∧R
ⓒ?
⇔∧?⊂?∧?∧R
∧TM
⊂?↓?ⓒ?⊂?
? TMⓒ∧?
I? TMⓒ∧?
∧TM
⊇∪
?%⇒
∧?ⓒ
%∨ ?.
♠?ⓒ
∈?ⓒR∧R
?⊂∪?
⇔∧TM
??R∈∧∨∪∈⇒
∈?? ∪TM
TM ∧R
ⓒ?
↓∨?⇔∪⊂TM%TM∪R ∧R
∈?? ∪TM
%TM
Rⓒ
%??∨R
∧∪
%∨TM ∪?I∨?⊇G .
?
′∪?⊇TM∨R∧∪∈?
??
#??R∧R
??R∈∧∨TM#??⊆ ?
??
#∨TM∈???R
# ∨∈? ?
?⇒I
#?∨?I I
?R∨⊂⇒∧?∧? .
?
′∪?⊇TM∨R∧∪∈?
??
#??R∧R
??R∈∧∨TM#??⊆ ?
??
#∨TM∈???R
# ∨∈? ?
?⇒I
#?∨?I I
?R∨⊂⇒∧?∧? .
?
≤?
#??R∧R
??R∈∧∨TM#??⊆ ?
??
#∨TM∈???R
# ∨∈? ?.
?
%ⓒ
#??R∪
?⊂∪?
∧TM
??R∈∧∨∪∈⇒
∈?? ∪TM
??
#∨G#R∪
ⓒ?
?ⓒ∧∪∈?∧?⇔∧??R
?#⇒
∧TMⓒ
∈?∧?⇔∈R ?⇔∧ ,
∧TMⓒ
?ⓒ∧∪#∨⇒⇔ #TM
???TM
?∨⊂⇒ ∪TM
?∧TM⊂TM
I∪?
ⓒ?
?#TM⊇R ↓?R
TM
∈ ⓒ ⓒTM
?∧ ↓ ⊂?∧TM .
♠?ⓒ
∧∨TM%TM%TM∪R ∧R
∧TM
⊂ ∈TM
∧TM
??R∈∧∨∪∈TM
∈?? TM
TM ∧R
ⓒ?
↓∨?⇔∪⊂TM%TM∪R ∧R
∧?ⓒ
G⊆TM TM
∈?∪
I∪?
???R
⇔ ⇔∈R G .
♠?
∧TM
? R∧R
⇔R
?R∪∧TM ∨I ?
⊂R
∨RI⊂Gⓒ?
↓G∨∪?.
♠?ⓒ
? R∧R
∧ %TM∧?
⊂G⇔?
⇔∧?ⓒ
R ⇔TM TM/G⊆TM TM
∧TM
?G∨?.
?
≤?
#??R∧R
??R∈∧∨TM#??⊆ ?
# ∨∈? ?
?⇒I
#?∨?I I
?R∨⊂⇒∧?∧? .
?
≤?
#??R∧R
??R∈∧∨TM#??⊆ ?.
?
∀#R∪
TM
?ⓒR⊂∪⇔∧ ∨?
I ∨ R∪
⊂R
⊂RI???
∧?↓ ∧?∧?
⊂#TM∨R
ⓒ?
#∨TM∈??G⇔R∪
∧∨? ⊂?∧∪⇔⊂⇒
?⊂∪?
⇔∧TM
⊂?↓?ⓒ?⊂?.
♠?ⓒ
R∈∧ ?R∧R
∧TM
G∨⊂?
?%R ?R ?
⇔∧TMⓒ
∈∨ TM
?G∨?
I∪?
⊂RI???
↓∨TMⓒ∪∈?
∪?⇔∧ ⊂?∧?.
∧?ⓒ
R⊂⊇?ⓒ∪⇔?R
?ⓒ ⊂?? ?
(⊂ ∨ ∪?
⇔?ⓒ
ⓒ?
∈? IR∧?∪
∈?∧∪
∈.?.%.)
⇔∧?⊂?∧ ⇔∧R
∧TM
∈?∪⊂?∧∪⇔∧∪∈⇒
⊂?↓?ⓒ?⊂?
∈?∪
I??∧R
∧TM
⊇∪
?%⇒
∧?ⓒ
%∨ ?
∈?R ⇔∧R
∧TM
∪?∈⇒%∧?.
∃
R%∪⇔∈R
?
∧TM%TM?G∧?⇔?
⇔R
???TM
⊂G∨TM
Rⓒ
%∨G%R∪
ⓒ?
I ⓒR∧?∪
?%⇒
∧TMⓒ
%R??∧?.
?
!⇒ⓒR∪
∈?∈⇒
⇔∧?ⓒ
IR ?.
?
%ⓒ
∧TM
⊂?↓?ⓒ?⊂?
⇔ ⓒR↓ ⇔R∪
ⓒ?
?R∪∧TM ∨IR
∈?∧
?#⇒
⊂?
∈?ⓒTMⓒ∪∈G
⇔ ⓒ? ∈R
⊂#TM∨R
ⓒ?
#∨TM∈??G⇔R∪
# ∨∈? ?,
?⊂∪?
∈.?.#.
R
⊂∪?
∧G∧TM∪?
#R∨ #∧ ⇔?
⇔ ⊂ TM ?R ?R ∧R
∧TMⓒ
G⊂#TM∨TM.
?
%ⓒ
R
I ⓒR∪
∈?ⓒTMⓒ∪∈?
⊂#TM∨R
ⓒ?
#∨TM∈??G⇔R∪
# ∨∈? ?,
??R∈∧∨TM#??⊆ ?,
∧∨? ⊂?∧∪⇔⊂⇒
?#⇒
#∧⇔?
∧TM
⊂?↓?ⓒ ⊂?∧TM ,
∪?∨∨TM
ⓒR∨TM
∈.?.#.
∀#∪∈TM∪ⓒ ⓒR ⇔∧R
⊂R
∧TMⓒ
G⊂#TM∨TM.
♠?ⓒ
RI∈?∧?⇔∧ ⇔R∧R,
⊂?ⓒ
?⊇?∪∨G⇔R∧R
∈?∪
R%?ⓒRI∈?∧?⇔∧ ⇔R∧R
∧TM
⊂?↓?ⓒ?⊂?
⊂⇒ⓒTM∪
⇔? .
?
(
?∈?∧??????
RI∈?∧?⇔∧?⇔?
⊂#TM∨R
ⓒ?
#∨TM∈??G⇔R∪
∪?∨∨TM ,
??R∈∧∨TM#??⊆ ?
# ∨∈? ?.
∂?∨?∈??R ⇔?R
ⓒ?
⇔ ⊂ TM ?R ?R ∧R
Gⓒ?
R⊆TM ⇔∪TM TM∧?⊂GⓒTM
G⊂#TM∨TM
Gⓒ?
R∪ ∪∈⇒
I∪?
∧?
∪? ∪∈?⇔ ?
∧?
RI∈?∧?⇔∧?⇔? .
↓R∧R
#⇒ ?
⇔?
⇒∧∪
TM∪
?? R
#TM
#∨TM∈ #∧TM ⓒ
?#⇒
?∈?∧??????
RI∈?∧?⇔∧?⇔?
Rⓒ
∈?? #∧TMⓒ∧?∪
?#⇒
∧?ⓒ
?⇔⊇??R∪?.
?
∃TM
∈?∪⊂?∧∪⇔∧∪∈⇒
⊂?↓?ⓒ?⊂?
#∨G#R∪
ⓒ?
RI∈?? ⇔∧?∧?∪
⇔R
R ∈TM??
#∨TM⇔ ?⇔∪⊂TM
↓∨TM.
&∪? #TM∧R
R#∪#∨⇒⇔?R∧?
?#?ⓒ?
#TM
?#?∪∧R ∧?∪
I∪?
∧?ⓒ
RⓒTM∪∈ ?⇔?
R∪ ∪∈TM
TM???∧∪∈TM
R⊆TM#?∪⇔⊂TM
R#∪ ?∨ ⓒR∪
∧TMⓒ
#R??∧?.
∂∨TM⊇ ??⊆R∪
RI∈?∧?⇔∧?⇔?
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